Q) Draw the necessary diagram for this question.

A man on the top of a lighthouse observes the angle of depression of two ships on the opposite sides of the lighthouse as 30° and 50° respectively. If the height of the lighthouse is 80m, find the distance between the two ships. Give your answer correct to the nearest meter. (Use Mathematical Tables for this Question)

ICSE Specimen Question Paper – 2026

Ans: Step 1:  Let’s make a diagram for the given question:

Step 2: Let’s start from Δ CPD, tan ∠CPD = tan 30° =

∴

∴ PD = 80 √3 m

Step 3: Next, we take in Δ CQD, ∵ ∠CQD = 50°

∴ ∠DCQ = 90° – 50° = 40°

∴ tan ∠DCQ = tan 40° =

∴ tan 50° =

∴ QD = 80 tan 50°

Step 4: Next, we can see from the diagram, that PQ = PD + QD

∴ PQ = 80 √3 + 80 an 50°

= 80 (√3 + tan 50°)

= 80 (1.7321 + 0.8391)

(from the math table, we get, tan 50°  = 0.8391 and √3 = 1.7321)

∴ PQ = 80 x 2.5712

∴ PQ = 205.696 m  = ~ 206 m

Therefore, distance between two ships is approx. 206 m.

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